UC-NRLF 


IflD 


' 

,0 


CIRCULAR 


OF   THE 


OFFICE  OF  THE  CHIEF  OF  ENGINEERS, 

XOVEMBER  28,  1881. 


PILE  FOUNDATIONS 

AND 

PILE-DEIVING  PORMULll, 


OFFICE  OF  THE  CHIEF  OF  ENGINEERS, 

UNITED  STATES  ARMY, 
Washington,  D.   C.,  November  28,  1881. 
CIRCULAR   | 
No.  17.     \ 

The  following  correspondence  respecting  pile  foundations  and 
pile-driving  formulae  is  communicated  to  the  Corps  of  Engineers. 

The  Chief  of  Engineers  approves  the  suggestions  contained 
in  Major  Weitzel's  letter  of  the  4th  of  October,  and  desires  that  the 
officers  of  the  Corps  will,  at  their  leisure,  communicate  to  this 
Office  any  views  they  may  have  on  the  subject  of  this  correspond- 
ence, which  he  deems  of  great  practical  importance,  and  also  the 
results  of  their  experiences  with  pile  foundations. 

He  also  desires  that  whenever  an  officer  of  the  Corps  has  oc- 
casion to  construct  a  pile  foundation,  he  will  cause  to  be  kept  an 
accurate  record  of  the  driving  of  the  piles,  embracing  the  kind, 
and  average  size  and  weight  of  the  piles,  the  weight  and  fall  of  the 
ram,  and  the  penetration  at  each  blow,  or  at  least  at  each  of  the 
last  (say  five)  blows,  a  copy  of  which  record  he  will  send  to  this 
Office  with  a  plan  of  the  foundation  on  which  is  marked  the  es- 
timated weight  each  pile  is  to  carry,  and  also  a  description  of  the 
soil. 

By  command  of  Brig.  Gen.  WRIGHT: 


Major  of  Engineers. 


286151 


UNITED  STATES  ENGINEER  OFFICE, 

Detroit,  Mich.,  August  4,  1881. 
Brig.  Gen.  H.  G.  WRJGHT, 

Chief  of  Engineers,  U.  S.  A., 

Washington,  D.  C. 
GENERAL : 

I  have  the  honor  to  acknowledge  the  receipt  of  a  reprint  of 
Paper  No.  5,  on  Practical  Engineering,  being  an  analytical  in- 
vestigation of  the  resistance  of  piles  to  superincumbent  pressure, 
deduced  from  the  force  of  driving,  &c.,  by  Brevet  Lieutenant 
Colonel  James  L.  Mason,  Captain  of  Engineers. 

This  reminds  me  that  it  must  be  my  duty  to  inform  the  officers 
of  the  Corps,  through  you,  of  my  experience  on  the  pile  and 
grillage  foundation  for  the  Martello  tower  at  Proctorsville,  La., 
although  this  information  has  not  been  called  for  by  you.  I  be- 
lieve, however,  that  all  the  official  records  of  this  work  were  lost 
by  a  fire  in  the  New  Orleans  Custom  House  or  through  the  civil 
war,  and  having  fortunately  preserved  a  few  private  notes  I  deem 
this  communication  of  some  interest  at  least. 

The  foundation  was  constructed  in  1856  and  1857. 

The  site  of  the  tower  at  Proctorsville,  as  determined  by  actual 
borings,  was  found  to  have  the  following  character,  viz.:  For  a 
depth  of  nine  feet  there  was  mud  mixed  with  sand,  then  followed 
a  layer  of  sand  about  five  feet  thick,  then  a  layer  of  sand  mixed 
with  clay  from  four  to  six  feet  thick,  and  then  followed  fine  clay. 
Sometimes  clay  was  met  in  small  quantities  at  the  depth  of  six 
feet,  as  well  as  small  layers  of  shells.  By  draining  the  site  the 
surface  was  lowered  about  six  inches. 

The  foundation  piles  were  driven  in  a  square  of  twenty  piles 
on  a  side,  four  feet  from  centre  to  centre.  Twenty-four  were 
omitted  to  leave  room  for  fresh  water  cisterns,  and  two  extra  ones 
were  driven  to  strengthen  supposed  weak  ones.  The  total  num- 
ber at  first  driven  was  therefore  378.  The  piles  were  driven  to 
distances  varying  from  30  to  35  feet  below  the  surface,  or  from 
10  to  1 5  feet  into  the  clay  stratum.  The  average  number  of  blows 
to  a  pile  was  55,  and  mainly  hard  driving.  After  all  these  piles 
were  driven,  ten  additional  ones  were  driven  at  different  points  to 
strengthen  supposed  weak  points.  Each  one  of  them  required 
over  loo  blows  to  drive  it. 

Before  beginning  the  foundation  I  drove  an  experimental  pile 
exactly  in  the  centre  of  the  site.  It  was  30  feet  long,  i2)4//X  1 2" 


at  top  and  nj^'Xu"  at  butt.  It  was  sharpened  to  a  bottom 
surface  about  4  inches  square.  Its  head  was  capped  with  a  round 
iron  ring.  Its  weight  was  1,611  pounds  and  the  weight  of  the 
hammer  was  910  pounds.  Its  own  weight  sank  it  5'  4",  and  it 
required  64  blows  to  drive  it  29'  6"  deeper.  The  fall  of  the 
hammer  at  the  first  blow  was  6  feet,  increasing  each  successive 
blow  by  the  amount  of  penetration,  excepting  the  last  ten  blows 
when  the  fall  was  regulated  to  exactly  5  feet  at  each  blow. 
The  penetrations  in  inches  were  as  follows  : 


This  pile,  according  to  Colonel  Mason's  formula,  should  have 
borne  52,556  pounds.  I  loaded  it  with  ^59,618  pounds  and  it  did 
not  settle.  I  afterwards  increased  the  load  to  62,500  pounds, 
when  it  settled  slowly.  The  greatest  weight  to  be  carried  by  any 
one  pile  was  between  30,000  and  35,000  pounds. 

The  tops  of  the  piles  were  sawed  off  on  a  level,  and  the  whole 
surface  between  them  covered  with  a  flooring  of  three-inch  planks 
tightly  fitted  in,  the  upper  surface  of  this  floor  being  flush  with 
the  tops  of  the  piles.  They  were  then  capped  in  one  direction 
by  stringers  i8//Xi8//  and  85'  long.  Each  of  these  stringers 
was  constructed  by  splicing  two  shorter  ones  of  equal  length  by 
means  of  the  regular  scarf  joint.  These  were  bound  together 
by  !2//Xi2//  stringers  85'  long  (formed  by  splicing  two  shorter 
ones)  running  over  the  line  of  piles  in  the  perpendicular  di- 
rection. These  i2"Xi2"  stringers  were  let  into  the  i8/xXi8x/ 
so  that  their  top  surfaces  were  flush.  In  the  little  squares  thus 
formed  and  next  to  the  iS//y^iS//  timbers,  were  laid  short  pieces 
!2//Xi2//  timbers,  and  the  intervals  filled  in  up  to  the  level  of 
the  latter  with  concrete.  The  whole  grillage  was  then  levelled  off 
with  short  pieces  of  6//Xi2//  planks.  This  grillage  was,  there- 
fore, 1  8  inches  thick.  Long  sheet  piling  was  driven  for  the  scarp 
of  the  wet  ditch,  the  upper  ends  resting  on  the  inside  of  the  string- 
ers on  the  outer  row  of  piles. 

In  order  to  distribute  the  weight  of  the  tower  uniformly  over 
this  foundation,  strong  reversed  groined  arches  were  turned,  the 
space  between  their  backs  and  the  grillage  being  filled  in  with 
solid  concrete  masonry. 

When  the  brick  work  of  this  tower,  which  was  carried  up  even 


on  all  sides,  was  about  half  completed  and  the  foundation  had  on 
it  less  than  half  the  load  it  was  designed  to  carry,  the  appropria- 
tion became  exhausted  and  the  work  was  stopped.  This  was  in 
the  spring  of  1858.  When  I  visited  the  work  about  six  months 
thereafter  I  found  a  marked  settlement.  The  four  salients  ap- 
parently remained  intact,  but  on  every  side  the  settlement  was 
about  the  same,  and  largest  about  the  middle,  so  that  the  courses 
of  brick  which  were  laid  perfectly  level  had  the  form  of  a  regu- 
lar curve. 

I  was  serving  at  that  time  as  assistant  to  Brevet  Major  G.  T. 
Beauregard,  Captain  of  Engineers.  In  addition  to  his  military 
works,  he  was  in  charge  of  the  construction  of  the  new  Custom 
House  in  New  Orleans,  La. 

In  order  to  ascertain  the  cause  of  this  settlement  he  directed 
some  experiments  to  be  made  by  the  architect  of  that  building, 
Mr.  Roy. 

I  do  not  remember  the  details  of  these  experiments.  I  was  on 
duty  at  forts  St.  Philip  and  Jackson,  and  afterwards  stationed  at 
West  Point  while  they  were  made.  The  civil  war  also  intervened. 
Subsequently,  however,  to  the  latter,  I  met  Mr.  Roy  and  he  told 
me  briefly  that  the  experiments  proved  that  piles  of  different 
cross-sections  driven  in  the  same  Louisiana  soil  and  under  ex- 
actly the  same  conditions,  do  not  have  a  power  of  resistance  pro- 
portional to  the  area  of  their  cross-section,  and  that  the  capacity 
of  resistance  per  square  inch  in  cross-section  of  pile  diminishes 
as  the  area  of  this  cross-section  becomes  greater.  That  is  to  say, 
a  pile  Af  square  in  cross-section  does  not  have  four  times  the 
resistance  to  pressure  of  one  2"  square.  This  decrease,  he  said, 
became  quite  marked  as  the  cross-section  of  the  piles  increased. 
He  believed  that  the  piling  for  the  foundation  at  Proctorsville  was 
driven  so  closely  that  the  whole  system  assumed  the  character 
of  a  single  pile  about  81  feet  square  in  cross-section  and  that 
therefore  its  capacity  of  resistance  per  square  foot  was  very  much 
reduced  as  compared  with  the  capacity  of  resistance  per  square 
foot  of  my  experimental  pile. 

I  have  never  since  had  an  opportunity  to  test  the  accuracy  of 
this  conclusion,  but  I  believe  that  some  of  the  officers  of  our 
Corps  are  so  situated  that  they  can  do  it,  hence  this  communica- 
tion. 

Very  respectfully,  your  obedient  servant, 

G.  WEITZEL, 
Major  of  Engineers. 


5' 

UNITED  STATES  ENGINEER  OFFICE, 

Detroit,  Mich.,  October  4,  1881. 
Brig.  Gen.  H.  G.  WRIGHT, 

Chief  of  Engineers,  U.  S.  A., 

Washington,  D.  C. 
GENERAL : 

I  have  the  honor  to  state  that  by  letter  to  you  dated  August  4, 
1 88 1,  I  acknowledged  the  receipt  of  a  reprint  of  Paper  No.  5  on 
Practical  Engineering,  being  an  analytical  investigation  of  the 
resistance  of  piles  to  superincumbent  pressure  deduced  from  the 
force  of  driving,  &c.,  by  Brevet  Lieutenant  Colonel  James  L. 
Mason,  Captain  of  Engineers. 

In  my  letter  I  informed  you  of  my  experience  on  the  pile  and 
grillage  foundation  for  the  Martello  tower  at  Proctorsville,  La. 

I  was  serving  at  the  time  this  foundation  was  constructed  as 
assistant  to  Brevet  Major  G.  T.  Beauregard,  Captain  of  Engi- 
neers. In  my  letter  I  referred  to  some  experiments  made  upon 
the  resistance  of  piles  in  that  soil  to  pressure,  made  by  Mr.  John 
Roy,  architect  of  the  New  Orleans  Custom  House,  the  erection 
of  which  was  also  in  charge  of  General  Beauregard. 

A  copy  of  my  letter  was  sent  from  your  office  to  General 
Beauregard  inquiring  if  any  records  of  these  experiments  were 
in  his  possession,  and  he  referred  it  to  Mr.  John  Roy.  In  reply 
the  latter  on  August  31,  1881,  enclosed  to  you  a  printed  table  of 
the  results  of  these  experiments.  On  September  i,  1881,  he  also 
enclosed  a  newspaper  article  bearing  upon  this  subject,  which  he 
had  contributed  to  the  New  Orleans  Times  of  July  10,  1879. 
Both  of  these  letters  were  referred  to  me  for  my  information,  and 
are  herewith  respectfully  returned. 

The  table  of  experiments  sent  by  Mr.  Roy  with  his  letter  of 
August  31,  and  the  result  of  the  experience  gained  at  Proctors- 
ville, La.,  show  conclusively,  it  seems  to  me,  that  although 
Mason's  rule  may  hold  good  for  an  isolated  pile,  it  cannot  be  de- 
pended upon  for  a  system  of  piles  such  as  are  driven  for  foun- 
dations. In  order,  therefore,  to  determine  the  factor  of  safety 
for  such  foundations,  the  views  and  experiences  of  the  officers  of 
corps,  it  seems  to  me,  would  be  valuable,  and  then  if  a  proper 
system  of  experiments  could  be  made  by  such  of  the  officers  as 
have  facilities  for  doing  so,  it  might  lead  to  practical  results  in 
solving  this  very  important  question. 

On  September  21,  1881,  Major  George  H.  Elliot  wrote  me  a 


private  letter  on  this  subject.  He  can  undoubtedly  furnish  you 
a  copy  of  it.  It  is  very  interesting,  and  the  conclusions  which  he 
arrives  at,  seem  to  me  very  practical. 

I  also  asked  a  brief  opinion  of  Lieutenant  Colonel  C.  B.  Corn- 
stock  on  the  general  subject  of  pile  driving,  without  mentioning 
to  him  the  special  case  which  produced  my  original  letter.  He 
has  authorized  me  to  use  his  reply.  It  is  as  follows  : 

"  The  energy  with  which  a  ram  strikes  the  head  of  a  pile  is 
spent  in  changing  the  form  of  the  pile,  of  the  ram,  in  heating 
them  and  making  them  vibrate,  and  in  most  cases  mainly  in 
overcoming  the  friction  of  the  earth  against  the  pile  and  in  mov- 
ing the  particles  of  the  earth  among  themselves,  thus  causing 
further  friction. 

"The  formulae  only  consider  the  resistance  during  the  very 
short  period  of  the  blow.  It  would  be  strange  if  such  resistance 
were  always,  for  all  soils,  the  same  as  when,  sometime  after  the 
pile  had  been  driven,  it  was  loaded  until  it  began  to  move.  Pos- 
sibly the  latter  resistance  is  sometimes  the  greater,  usually  it  is 
doubtless  much  less,  for  most  materials  require  a  less  force  to 
change  their  form  slowly  than  rapidly.  A  substance  like  clay, 
that  fs  plastic,  might  resist  driving  piles  very  strongly  and  yet 
furnish  a  very  much  smaller  resistance  to  a  permanent  load. 
Not  knowing  the  relation  of  the  two  resistances,  a  formula  which 
does  not  include  that  relation  (i.  <?.,  the  character  of  the  soil), 
may  be,  even  for  isolated  piles,  much  in  error.  The  only  way  to 
get  a  reliable  formula  seems  to  be  to  determine  for  characteristic, 
well  defined,  and  carefully  described  soils,  the  ratio  between  the 
resistances  given  by  some  good  formula  like  Rankine's,  and  the 
actual  load  which  will  start  the  pile  very  slowly  down  and  keep 
it  going. 

"In  soft  material  a  certain  load  spread  over  the  surface  will 
carry  the  whole  of  it  down  bodily  to  considerable  depths.  As 
soon  as  a  sufficient  number  of  piles  in  this  area  are  driven  and 
loaded,  they  will  do  the  same,  and  additional  piles  are  useless. 
In  such  a  case  the  economical  intervals  for  piles  could  only  be 
found  by  experience."  » 

I  submit  herewith  Mr.  Roy's  table  of  experiments  : 


A  table  of  experiments  on  the  compressibility  of  soil  of  New  Or- 
leans, La.,  made  by  Mr.  John  Roy,  in  the  years  1851  and  1852. 


I    Size  of  bearing,  in 
square  inches. 


Weight  '  S~-3 
in  pounds,  ^  y  § 
applied.  •& 


1 

o 
Z 

|  ST.- 

C 

c/2 

|8B 

n.  u  u 

ifljj 

I 

xx  y<=    A 

6-375 

102.000 

3M 

3° 

12 

1760 

2 

MX    M==     K 

25.500 

IO2.OOO 

7 

3° 

12 

1760 

3 

Kx   K~    ts 

57-375 

102.000 

ii 

30 

12 

1760 

4 

i     X        =i 

102.000 

IO2.OOO 

ii 

3° 

12 

1760 

5 

i     X         ==     i 

IO2.OOO 

IO2.OOO 

ii 

3° 

12 

1760 

6 

I       X       %=      2% 

293.250 

102.000 

263^ 

3° 

12 

1760 

7 

4     X         =•  16 

l632.000 

IO2.OOO 

78 

3° 

12 

1760 

8 

i     Xi       =16 

1632.000 

IO2.OOO 

33 

3° 

12 

1760 

9 

4     X         =  16 

1632.000 

102.000 

120 

161 

48 

1760 

10 

*A  x    K  =    iV 

I.I25 

iS.OOO 

/^ 

3 

12 

1760 

ii 

i^x      =    y± 

4.500 

18.000 

H 

3 

12 

1760 

12 

MX      ==     M 

9.000 

iS.OOO 

g 

3 

12 

1760 

*3 

Kx      =    K 

13.500 

iS.OOO 

3 

12 

1760 

14 

i     X        =i 

iS.OOO 

iS.OOO 

^ 

12 

1760 

15 

36.000 

36.000 

2M 

51 

12 

1760 

16 

2ix      ==    % 

27.000 

36.000 

1% 

51 

12 

1760 

i-j 

MX      =     M 

18.000 

36.000 

JK 

12 

I76o 

18 

zMx      =  40 

642.000 

16.050 

7* 

99 

6 

1760 

'9 

i     X         =4 

170.000 

42.500 

% 

42 

O 

I76o 

20 

6     Xi       =i44 

2552.000 

17.720 

5^ 

107 

0 

400 

21 

6    Xi       =M4 

3362.400 

23-350 

A 

182 

0 

400 

22 

6     X24     =288 

15580.000 

54-°97 

i 

48 

o 

300 

23 

20^X20^=432 

18703.000 

43  -3°° 

26 

96 

400 

24 

12       XI2       =144 

5132.000 

35-640 

% 

20 

96 

400 

25 
26 

24     X24     =576 
Weight  increased. 

23150.000 
45724.000 

40.203 
79-38o 

13^ 

38 
40 

$ 

300 

300 

27 

Weight  increased. 

57600.000 

IOO-OOO 

iS1^ 

55 

36 

300 

28 

i     X  i     —     i 

IO2.OOO 

IO2.OOO 

6 

68 

48 

333 

29 

Weight  increased. 

2O2.OOO 

202.000 

18 

121 

48 

333 

3° 

4     X  4     =  16 
Weight  increased. 

1632.000 
3232.OOO 

IO2.OOO 
2O2.OOO 

54M 

68 

121 

48 

48 

333 
333 

S2 

i     X  i     =     i 

102.000 

102.000 

I 

49 

48 

300 

33 

Weight  increased. 

2O2.OOO 

2O2.OOO 

7 

87 

48 

300 

j> 
35 

4     X  4     =16 
Weight  increased. 

1632.000 
3232.000 

IO2.OOO 
202.000 

7 

i; 

48 

48 

300 
300 

NOTES. — Nos.  23  and  24  were  made  at  the  new  Custom  House,  by  a  Commission  of 
U.  S.  Engineers,  appointed  by  the  Treasury  Department. 

It  will  be  seen,  by  the  above  table,  that,  contrary  to  the  general  opinion,  a  larger 
surface  sinks  more  than  in  proportion  to  its  area. 

A  very  interesting  article  on  this  subject  appears  in  the  num- 
ber of  Van  Nostrand's  Engineering  Magazine  for  October,  1881. 
It  is  entitled  "Note  on  the  Friction  of  Timber  Piles  in  Clay"  by 
Arthur  Cameron  Hertzig,  Assoc.  M.  Inst.  C.  E. 
Very  respectfully,  your  obedient  servant, 

G.  WEITZEL, 
Major  of  Engineers. 


WASHINGTON,  D.  C., 

November  23,  1881. 
Brig.  Gen.  H.  G.  WRIGHT, 

Chief  of  Engineers,  U.  S.  A. 
GENERAL: 

In  compliance  with  your  request,  I  have  the  honor  to  enclose 
herewith  a  copy  of  the  letter  referred  to  in  General  Weitzel's  let- 
ter to  you  of  the  4th  ultimo. 

It  is  proper  for  me  to  add  that  I  have  taken  advantage  of  the 
delay  in  the  printing  of  the  letters  of  General  Weitzel,  to  add  the 
formulas  referred  to  in  my  letter,  and  such  remarks  as  have  been 
suggested  by  further  consideration  of  the  important  question 
presented  by  him. 

Very  respectfully,  your  obedient  servant, 

GEORGE  H.  ELLIOT, 

Major  of  Engineers. 


Major  Elliot  to  General  Weitzel. 

Washington,  D.  C.,  2ist  September,  1881. 

Your  letter  of  the  4th  of  August  to  the  Chief  of  Engineers,  rela- 
ting your  experience  in  the  foundation  of  the  Martello  tower  at 
Proctorsville,  La.,  has  suggested  a  comparison  of  the  pile  driv- 
ing formulae  accessible  to  me. 

Assuming,  in  these  formulae,  the  case  of  the  test  pile  at  Proc- 
torsville, which  was  thirty  (30)  ftet  long,  twelve  (12)  by  twelve 
and  one-half  ( 12^  )  inches  at  top,  eleven  (i  i)  by  eleven  and  one- 
half  ( 1 1 K )  inches  at  bottom  ;  which  weighed  sixteen  hundred 
and  eleven  (i,6n)  pounds,  and  was  driven  by  a  ram  weighing 
nine  hundred  and  ten  (910)  pounds,  falling  five  (5)  feet  at  the  last 
blow ;  the  last  blow  driving  the  pile  three-eighths  ( y% )  of  an 
inch,  the  discrepancies  between  the  results  are  remarkable.  The 
extreme  supporting  power  of  this  pile,  obtained  from  some  of 
these  formulae,  is  as  follows  : 

Pounds. 

Nystrom 18,971 

Mason 52,  556 

Weisbach 52,  556 

Trautwine 58,  302 

Rankine* 128,509 

Major  Sanders'  formula  does  not  give  the  extreme  supporting 
power  of  the  pile,  but  the  safe  load  only — in  this  case,  18.200 
pounds.  McAlpine's  formula  in  this  case  gives  a  negative  re- 
sult, as  it  always  does  when  W+  .228  y  F  is  less  than  i,  ^rep- 
resenting the  weight  of  the  ram  in  tons,  and  .Fits  fall  in  feet. 

Assuming  another  case,  a  case  in  which  the  weight  and  fall  of 
the  ram  are  much  greater,  the  discrepancies  are  still  more  remark- 
able. Say  that  the  pile  is  of  the  same  size  and  weight  as  the  one 
at  Proctorsville  ;  that  it  makes  the  same  penetration  at  the  last 
blow,  and  is  driven  by  a  two  thousand  (2,000)  pound  ram,  fall- 
ing twenty-five  (25)  feet.  The  extreme  supporting  power  and 
safe  load  in  this  case,  according  to  the  various  authorities,  are 
stated  in  the  following  table,  in  which,  you  will  observe,  the  rela- 
tive positions  of  the  names  of  these  authorities  are  not  the  same 
as  in  the  preceding  table. 

*  Assuming  the  modulus  of  elasticity  to  be  750  tons. 


10 


I  Extreme      sup- 
Names  of  authors  of  formulas       porting  power  Safe   load  in 
and  rules.  !     of  the  pile  in!     pounds, 

pounds. 


McAlpine  (1) 185,069  61,689 

Trautwine  (2) 219,117  73,079 

Hodgkinson  (3) 403, 450  40, 345 

Nystrom  (4) 490,824  81,804 

Rankine  (5) '     810,  ooo(6)  ;         81,000 

Do.      (7) 851,200  130,954 

Mason(8) 886,080  221,520 

Weisbach(9) |         886,080  48,739 

The  Dutch  Engineers  (10)   .    .    .1         886,080  110,760 

Stevellyl11) |         886,080  .... 

Sanders  (12) I 200,000 

Haswell(13) j 200,000 

Rondelet(14) : 69,375 

PerroneU15) ! 125,802 

Rankine  (1G) 150,000 

Mahan(17) 150,000 

Wheeler  (18) 150,000 

Rankine  (19) 30,000 

Mahan(20) ' 30,000 

Wheeler  (21) 30,000 


(!)  McAlpine's  formula  is  P  —  80  (W  +  .228  y  F — 1\,  in  which  P  represents  the  ex- 
treme supporting  power  of  the  pile  in  tons,  Wthe  weight  of  the  ram  in  tons,  and  ./''its 
fall  in  feet.  (Journal  of  the  Franklin  Institute,  sd  series,  Vol.  LV.).  His  co-efficient 
of  safety  is  ^- 

(2)  Trautwine's  formula  is  P  = — — ,  in  which  P  and  F  are  the  same  as 

in  McAlpine's  formula;  J^the  weight  of  the  ram  in  pounds,  and  /,  the  penetration 
at  the  last  blow,  in  inches.  His  co-efficients  of  safety  are  from  i^  to  V2,  "  according  to 
circumstances."  In  this  case  and  in  similar  cases,  I  have  assumed  the  arithmetical 
mean.  In  this  case,  y$. 

(3)  This  case  supposes  that  the  pile  is  driven  to  the  hed  rock  through  soft  mud,  and  is 
not  supported  at  the  sides.     I  have  assumed  in  Hodgkinson's  rule  (Mahan's  Civil  En- 
gineering, p.  80),  T]JJ  as  a  co-efficient  of  safety. 

11/3  JS 

(4)Nystrom's  formula  is  P== —  ,    in  which  P  represents  the  extreme  sup- 

/  (  Vy  x  ivy 

porting  power  of  the  pile  in  pounds  ;  Wine  weight  of  the  ram,  and  7t/the  weight  of  the 
pile — both  in  pounds;  J^the  fall  of  the  ram,  and  p  the  penetration  at  the  last  blow. 
His  co-efficient  of  safety  is  %. 

(5)  Rankine  has  a  rule  that  "  the  factor  of  safety  against  direct  crushing  of  the  tim- 
ber should  not  be  less  than  10." 

(6)  Resistance  of  the  pile  to  crushing. 

(7)  Assuming  in  \a&  formula  the  modulus  of  elasticity  to  be  750  tons.     His  formula  is 

^— '' \l  — —  +  --    -—- iLf-li!    in  which  P  represents  the  extreme  support- 


II 

These  discrepancies  show  that  some  of  these  formulae,  or,  at 
least,  some  of  their  factors  of  safety*  are  misleading,  and  it 
seems  to  me  that  all  of  them  which  have  not  been  based  upon 
experiments  on  the  capacity  of  soils  to  sustain  pressures,  must 
be  so. 

Let  us  see  what  supports  a  loaded  pile. 

I  conceive  that  there  is  below  the  bottom  of  the  pile  in  orcli- 

ing  power  of  the  pile  in  tons;  W  the  weight  of  the  ram,  and  e  the  modulus  of  elas- 
ticity, both  in  tons;  .Fthe  fall  of  the  ram,  /  the  length  of  the  pile,  and  /  the  penetra- 
tion at  the  last  blow,  all  in  feet,  and  s  the  average  section  of  the  pile  in  square  inches. 
His  factors  of  safety  for  use  with  his  formula  are  "from  3  to  10." 

UTI  p 

(8) Colonel   Mason's  formula  is    P=— x  —   ,   in  which  P  represents  the  ex- 

W+iv      f 

treme  supporting  power  of  the  pile ;  W  the  weight  of  the  ram ;  iv  the  weight  of  the 
pile ;  F  the  fall  of  the  ram,  and  p  the  penetration  at  the  last  blow.  His  factor  of 
safety  at  Fort  Montgomery  was  4. 

(9)  Weisbach's  formula   is    the  same  as  Mason's.     His  co-efficients  "for  duration 
with  security"  are  from  T^  to  ^,  the  arithmetical  mean  of  which  is  Tg/jg. 

(10)  Quoted  in  Proceedings  of  the  Institution  of  Civil  Engineers  (British),  Vol.  LXIV. 
Their  formula  is  the  same  as  Mason's.     Their  factors  of  safety  are  from  6  to  10.     I 
have  assumed  the  arithmetical  mean  of  these,  to  find  the  mean  co-efficient  of  safety. 

It  may  be  a  question  in  this  case,  whether  the  mean  co-efficient  of  safety  should  be 
r.V  7.7J  or  B-  T.H  is  tne  geometrical  mean  of  J-  and  ^,  which  are  the  co-efficients 
of  safety  corresponding  to  the  extreme  factors  of  safety,  and  it  was  used  by  the  En- 
gineer of  the  Portsmouth  (England)  Docks,  as  a  mean  co-efficient,  to  find  the  safe 
value  of  P  for  the  piles  of  his  work,  from  the  formula  and  factors  of  safety  of  the 
Dutch  Engineers.  A  similar  doubt  arises  in  finding  a  mean  co-efficient  of  safety  from 
Rankine's  factors  of  safety. 

(n) Quoted  in  Thomas  Stevenson's  "Design  and  Construction  of  Harbours."  His 
formula  is  the  same  as  Mason's.  No  factor  of  safety  is  given. 

(12)  The  extreme  supporting  power  of  a  pile  is  not  given  in  the  formula  of  Major  Sanders, 
which  he  contributed  to  the  Journal  of  the  Franklin  Institute  and  which  may  be  found 

in  Vol. XXII.,  (3rd  Series).  The  formula  is  P  =. —    ,     in  which  /'represents  the  safe 

° P 
load  of  the  pile,  /'the  fall  of  the  ram,  and/  the  penetration  at  the  last  blow. 

(13)  Major  Sanders'  formula  adopted  by  Haswell. 

(14)  427  to  498   pounds   to   the  square  inch  of  head  of  pile.     Quoted  in  Professor 
Vose's  "Manual  for  Railroad  Engineers." 

(18)  From  his  rule  found  in    (Euvres  de  Perronet.    "Nous  estimons,  pour  ces  rai- 
sons,  que  I'  on  ne  doit  point  cltarger  les  pilots  de  8  a  q  pouces  de  grosseur,  de  plus  de 
cinquante  milliers  ;  ceux  d'un  pied,  de  plus  de  cent  milliers  ;  et  ainsi  des  autres  a 
proportion  du  quarre  de  leur  diametre  ou  de  la  superficie  de  leur  tete." 

i  millier  —  1079.22  pounds,  i  pied=  12.8". 
(16)  1,000  pounds  to  the  square  inch  of  head  of  pile. 
(")  The  same. 
(18)The  same. 

(19)  "  Piles  standing  in  soft  ground  by  friction." 

(20) "  Piles  which  resist  only  in  virtue  of  the  friction  arising  from  the  compression  of 
the  soil." 

(*')  "  When  they  resist  wholly  by  friction  on  the  sides." 

*  By  the  term  "factor  of  safety,"  which  is  used  by  many  of  the  authorities  on  foun- 
dations, is  meant  the  number  which  is  to  be  multiplied  into  the  working  load,  in  any 
case,  to  find  the  "  extreme  supporting  power"  of  the  pile,  or  the  resistance  of  the 
soil,  to  which,  for  safety  in  that  case,  the  pile  is  to  be  driven. 

The  term  "  co-efficient "  of  safety  is  used  by  McAlpine.  It  is  a  fraction  which  is  to 
be  multiplied  into  the  "  extreme  supporting  power"  of  a  pile  to  find  its  safe  load.  It 
is  the  reciprocal  of  the  corresponding  "factor  of  safety." 


12 

nary  soils,  a  conoidal  mass  of  earth,  a,  b,  r,  d,  (Fig.  I.)  the 
particles  of  which  are  acted  upon  by  pressures  derived  from  the 
weight  of  the  pile  and  its  load,  and  the  form  and  dimensions  of 
which,  depend  on  this  weight  and  on  the  kind  of  soil ;  *  that  at 
every  section  e,f;  e,f,  of  the  pile  below  the  surface  of  the  ground, 
the  particles  of  earth  in  contact  with  the  pile,  are,  by  reason  of 
friction,  pressed  downward,  and  that  these  pressures  are  distrib- 
uted (spread)  in  the  same  way  that  the  pressure  at  the  foot  of  the 
pile  is  distributed  ;  that  is,  through  the  particles  of  the  earth  sur- 
rounding the  pile,  which  are  limited  by  conoidal  surfaces,  of 
which,  (in  homogeneous  soils,)  the  pile  is  a  common  axis.f 

Are  the  particles  of  earth  within  these  conoids  of  pressure  and 
distant  from  the  pile,  acted  upon  by  the  blows  of  the  ram  ? 

General  Tower,  in  remarking  upon  a  recent  device  by  a  citi- 
zen of  Virginia,  for  an  armor  protection  of  fortifications,  consist- 
ing of  a  thin  iron  or  steel  plate  backed  by  springs,  said  that  even 
if  the  plate  were  one  foot  thick,  suspended  by  chains,  and  with- 
out any  backing  whatever,  it  would  be  penetrated  by  a  shot  from 
an  8 1 -ton  gun  in  about  -j-^  of  a  second,  and  before  the  plate 
could  move  perceptibly. 

Is  it  not  probable,  reasoning  from  analogy,  that  the  blows  of 
the  ram  upon  the  head  of  a  pile  reach  only  the  particles  of  earth 
which  are  in  contact  with  or  very  near  the  foot  and  the  sides  of 
the  pile;  that  the  action  (occupying  only  a  small  fraction  of  a 
second)  is  too  quick  to  be  communicated  to  more  distant  par- 
ticles composing  the  conoids  of  pressure,  and  that  subsequently 
the  forces  which  hold  these  particles  in  place  may  be  disturbed, 
and  the  particles  may  yield,  under  continued  pressures  commu- 
nicated successively  through  the  pile,  and  the  particles  of  earth 
in  contact  with,  and  near  the  pile  ? 

It  might  appear  at  first  sight,  that  if  pressures  are  more  dis- 
tributed laterally  in  the  earth  below  and  around  a  pile,  the  resis- 
tance to  pressures  must  be  greater  than  the  resistance  to  blows, 
but  the  truth  is,  that  it  cannot  be  said  that  one  is  greater  or  less 


*None  of  (he  books  available  for  reference,  throw  any  light  on  this  subject.  Ran- 
kine  has  a  theory  concerning  the  pressures  within  an  earthen  mass  derived  from  its  own 
weight,  but  he  gives  no  results  of  experiments  (if  any  have  been  made),  touching  the 
action  of  earth  under  exterior  pressures. 

fin  sticky  soils,  no  doubt,  the  action  of  the  particles  of  earth  adjoining  a  pile,  is,  in 
part,  one  of  drawing  or  pulling  downward  the  particles  of  earth  exterior  to  them,  and 
the  distance  to  which  this  action  extends,  depends  on  the  degree  of  adhesion  of  these 
particles. 


13 

than  the  other,  except  by  empirical  comparisons  between  the 
effects  of  blows  and  the  results  of  pressures. 

When  these  comparisons  in  the  case  of  any  kind  of  soil  have 
been  made,  the  true  relation  between  these  effects  and  these  re- 
sults may  be  discovered,  and  correct  and  reliable  factors  of  safety 
for  use  with  formulae  for  the  sustaining  power  of  piles,  into  which 
formulae  enter  the  terms  common  to  all  pile  driving  formulae, 
(viz.,  the  weight  of  the  ram,  its  fall,  and  the  average  penetration 
of  the  last  blows,)  may  be  made  for  that  kind  of  soil,  but  I  think 
it  evident  that  no  pile  driving  formula  or  factors  of  safety  based 

only  on  theoretical  deductions  from  the  formula  Ps  =  i —,     can 

2 

be  relied  on,  even  for  single  isolated  piles,  or  for  piles  driven  at 
considerable  distances  apart. 

Now  let  us  examine  the  case  of  an  ordinary  pile  founda- 
tion in  any  compressible  soil.  Say  that  the  piles  are  driven  three 
(3)  feet  apart,  in  rows  the  same  distance  apart,  from  centre  to 
centre. 

Would  a  safe  load  for  this  foundation  be  equal  to  the  safe  load 
of  a  single  isolated  pile  in  that  soil,  multiplied  by  the  number  of 
piles  ? 

I  think  not,  for,  if  it  be  true  that  below  and  surrounding  the 
piles,  there  exist  within  the  soil  the  conoids  of  pressure  before 
alluded  to,  and  if  the  surfaces  of  these  conoids  make  any  con- 
siderable angle  with  the  vertical,  then  the  pressure  upon  the 
earth  below  and  between  the  piles,  may  be  much  greater  in  the 
case  supposed,  than  in  the  case  of  an  isolated  pile. 

Let  Fig.  2  represent  a  plan  of  the  piles  of  this  foundation,  and 
let  Fig.  3  represent  a  section  through  one  of  the  rows.  Let  a,  b, 
c,  d,  Fig.  3,  represent  a  section  through  the  axis  of  the  conoid  of 
pressure  arising  from  the  pressure  of  the  pile  and  its  load,  at  the 
foot  of  the  pile  A,  and  let  a' t  &',  c' ,  d',  represent  a  similar  sec- 
tion through  the  conoid  of  pressure  at  the  foot  of  the  pile  B. 
Let  us  pass  a  horizontal  plane  at  any  short  distance — say  eighteen 
(18)  inches — below  the  feet  of  the  piles  (\\;hich  we  suppose  to  be 
driven  to  a  uniform  depth),  and  let  z,  z,  it  z,  and  k,  k,  k,  k,  Fig. 
2,  represent  in  plan,  and  let  m,  n,  and  m',  n' ',  represent  in  sec- 
tion, the  areas  cut  from  the  conoids  of  pressure  by  this  plane, 
and  it  will  be  seen  that  considerable  portions  of  each  of  these 
areas,  may  be  acted  upon  by  pressures  derived  from  both  of  the 
piles  and  their  loads.  The  same  may  be  said  of  the  earth  within 


H 

the  conoids  of  pressure  surrounding  the  piles,  and  it  appears 
therefore,  that  the  forces  acting  upon  the  particles  of  earth  be- 
low and  surrounding  a  pile,  may  be  in  equilibrium,  and  the  par- 
ticles may  be  at  rest,  in  the  case  of  a  loaded  isolated  pile,  when 
the  equilibrium  may  be  disturbed,  and  the  particles  may  sink 
with  the  pile,  when  the  same  load  per  pile  is  laid  upon  a  founda- 
tion composed  of  piles  driven  in  the  same  soil  at  such  distances 
apart  that  their  conoids  of  pressure  intersect  each  other. 

McAlpine,  before  constructing  the  Brooklyn  Dry  Dock,  made 
experiments  with  loads  upon  piles, *  and  of  his  formula  he  says  : 

"The  co-efficient  is  reliable  for  such  material  as  was  found  at 
that  place." 

This  material  was  "a  silicious  sand  mixed  with  comminuted 
particles  of  mica  and  a  little  vegetable  loam,  and  was  generally 
encountered  in  the  form  of  quicksand." 

McAlpine  also  says  : 

"It  is  very  desirable  that  similar  experiments  should  be  made 
in  soils  of  different  kinds,  which  would  make  this  formula  ap- 
plicable to  all  the  cases  usually  met  with  in  constructions." 

Major  Sanders  experimented  by  loading  sets  of  piles  of  four 
each,  and  Colonel  Mason  made  his  formula  when  the  fort  (Mont- 
gomery) which  he  was  constructing  on  a  pile  foundation,  had 
been  nearly  completed. 

Which  of  the  other  pile  driving  formulae  and  factors  of  safety 
given  by  the  authorities  I  have  quoted,  were  deduced  from  exper- 
iments in  loading  more  than  single  isolated  piles,  I  do  not  know, 
but  some  of  the  formulae  appear  to  have  been  based  only  on 
theoretical  considerations,  and  some  of  the  factors  of  safety  ap- 
pear to  be  simply  conjectural. 

None  of  the  formulas  are  accompanied  by  tables  of  factors  of 
safety,  corresponding  to  specified  kinds  of  soil. 

It  is  factors  of  safety  that  are  most  needed.  There  are  many 
formulas.  Doubtless  most  of  them  are  good,  and  one  of  them, — • 

P= __X , — has  been  worked  out  independently  by  seve- 

W+w     p 

ral  distinguished  authors ;  but  can  any  of  them  be  used  safely 
and  confidently,  when  the  factors  of  safety  furnished  by  the 
authors  of  these  formulas  produce  results  so  discordant  ? 


*As  far  as  I  can  determine  from  his  paper  read  before  the  Franklin  Institute,  Jan- 
uary 15,  1868,  these  experiments  were  made  (by  means  of  a  lever),  upon  isolated  piles 
only. 


15 

An  Engineer  having  to  construct  a  pile  foundation,  must 
take  some  pile  driving  formula  and  factor  of  safety,  as  he 
finds  them.  He  has  no  time  to  make  proper  experiments  in  the 
soil  he  has  to  deal  with,  for  that  would  require  years  of  time. 

It  is  not  enough  for  his  purpose  that  an  author  of  a  formula 
prescribes  for  use  with  it,  a  single  factor  of  safety  of  3,  or  of  4,  for  he 
knows  that  that  factor  can  only  be  a  proper  one  for  one  kind  of 
soil,  and  he  is  not  told  what  the  kind  of  soil  is.  It  may  be  more, 
or  it  may  be  less  easily  penetrated  than  his  own.  In  the  former 
case,  by  the  use  of  an  unnecessarily  large  factor  of  safety,  he  would 
make  his  foundation  unnecessarily  expensive  ;  and  in  the  latter, 
his  foundation  would  be  in  danger  of  yielding,  sometime,  under 
its  load.  Neither  is  he  satisfied  .to  be  told  to  use  a  factor  of  safety 
from  3  to  10;  from  6  to  10,  or  from  10  to  100,  "according  to  cir- 
cumstances." He  wants  his  own  case  and  its  proper  factor  of 
safety  to  be,  as  far  as  possible,  definitely  stated,  or  else,  it  seems 
to  me,  he  would  prefer  to  drive  the  piles  of  his  foundation  in 
every  case  of  importance,  as  far  as  they  will  go,  or  to  the  equiv- 
alent of  their  "absolute  stoppage,"*  which,  he  knows,  would  make 
his  foundation  as  safe  as  a  pile  foundation  can  be  made,  though 
it  may  be  expensive. 

I  chink  that  the  want  of  reliable  and  definite  factors  of  safety 
can,  in  a  manner  be  supplied,  without  waiting  for  experiments 
made  for  the  purpose. 

While  it  is  difficult,  no  doubt,  to  make  minute  descriptions  of 
soils  by  giving  the  proportions  of  their  physical  constituents,  I 
think  that  a  table  of  useful  factors  of  safety,  corresponding  to 
quite  a  large  number  of  the  ordinary  and  easily  recognizable  soils, 
could  be  made  for  use  with  any  good  formula,  say  Mason's,  from 
the  past  recorded  experiences  of  the  officers  of  the  Corps  of  En- 
gineers. This  could  be  done  by  dividing  the  values  of  P  de- 
duced from  that  formula,  (substituting  in  each  case  for  W,  F,  u>, 
and/,  the  actual  weight  and  fall  of  the  ram,  the  average  weight 
of  the  piles,  and  the  average  penetration  at  the  last  blows)  by  the 
actual  weights  of  the  structures  per  pile. 

A  comparison  of  all  the  factors  of  safety,  obtained  in  this 
way,  which  would  arise  from  cases  in  which  foundations  in  any 


sand  (-2000}  pound  ram,  falling  twenty-five  (25)  feet,  would  sink  a  sixteen  hundred  and 
eleven  (1611)  pound  pile,  one  (i)  inch. 


i6 

specified  kind  of  soil  have  carried  their  loads  for  some  years 
without  any  evidence  of  settling,  would  probably  show  that  no 
two  of  them  would  be  precisely  the  same,  and  that  some  of  them 
would  be  excessive.  These  latter,  which  would  lead  to  unneces- 
sarily expensive  work,  and  any  inadequate  factor  which  might 
be  developed  by  a  failure  of  a  foundation,  like  the  one  at  Proctors- 
ville,  to  carry  its  load,  could  be  rejected.  A  fair  judgment  could 
then  be  taken  in  respect  of  the  others,  and  a  single  safe  and  re- 
liable factor  for  that  kind  of  soil,  could  be  determined  on. 

From  the  foregoing  considerations,  I  come  to  the  following 
conclusions: 

ist.  Pile  driving  formulae  should  be  accompanied  by  tables  of 
factors  of  safety,  corresponding  to  all  the  common  and  easily 
recognizable  kinds  of  soil. 

2nd.  These  factors  of  safety  should  be  determined  on  after  ex- 
tended experiments  on  the  supporting  power  of  piles,*  although 
approximate  factors  v/hich  could  be  used  without  hazard,  could  be 
found  from  examinations  of  the  records  of  the  driving  of  the 
piles  of  actual  foundations,  provided  the  weights  of  the  super- 
structures are  known,  and  descriptions  of  the  soils  have  been  pre- 
served; and  provided  also,  that  the  foundations  have  carried 
their  loads  during  sufficient  lengths  of  time. 

3rd.  In  experiments  on  the  supporting  power  of  piles,  the 
loads  should  not  rest  upon  single  isolated  piles,  but  they  should 
cover  a  number  of  piles,  driven  at  those  distances  apart  which 
are  usual  in  pile  foundations. 

4th.  In  every  case  of  construction  of  a  pile  foundation,  the 
record  of  the  driving  of  the  piles,  should  include  such  a  descrip- 
tion of  the  soil,  obtained  from  borings,  as  would  enable  an  En- 
gineer, having  to  found  a  work  in  a  similar  soil,  to  recognize  it. 

*The  case  mentioned  by  you  shows  that  the  testing  by  loading  should  extend  over 
considerable  lengths  of  time.  Even  the  foundations  of  Fort  Montgomery  and  Fort 
Delaware  have  settled  more  or  less. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $I.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


